Suppose that X1, X2 and X3 are independent discrete random variables defined on the set {0, 1}. Let.

Suppose that X1, X2 and X3 are independent discrete random variables defined on the set {0, 1}. Let i denote the bias of Xi , for i = 1, 2, 3. Prove that if X1 ? X2 is independent of X2 ? X3, then either 1, 3 = 0 or 2 = ±1/2. (e) For AES-128 answer the following questions: i. In one sentence answer, why is Boomerang attack expected to be more powerful than a conventional Differential attack? ii. Consider two keys of AES-128, which are related as: their differential value is (a, 0, 0, 0), where a is a given 32-bit value 6= 0. Determine the propagation of the 4-round differentials of the round keys through the key scheduling algorithm.